Energy, Exergy, and Economic (3E) Analysis of SOFC-GT-ORC Hybrid Systems for Ammonia-Fueled Ships

Abstract

A feasible solid oxide fuel cell–gas turbine–organic Rankine cycle (SOFC-GT-ORC) hybrid system for ammonia-fueled ships is presented in this study. To confirm the quantitative changes in thermodynamic performance and economics according to the system configuration, the system using ammonia fuel was simulated, and energy, exergy, and economic (3E) analyses were performed. As a result, the system economics generally had an inversely proportional relationship with the thermodynamic performance. System optimization was performed using a multi-objective genetic algorithm, setting the conflicting thermodynamic performance and economics as objective functions. The key results of this study obtained through optimization are as follows. With the introduction of the ORC, the SOFC-GT hybrid system thermal efficiency was increased by 2–6%, but the cost increased by 14–24%. In the SOFC-GT-ORC hybrid system, preferentially reducing the irreversibility of the SOFC, combustor, and ORC evaporator is advantageous in terms of performance. It is economical to use a moderate amount of SOFC fuel to achieve the target output; the cost of the ORC in the SOFC-GT-ORC hybrid system was approximately $23/h. This study is unique in that it systematically conducted a 3E analysis, which had not been previously well-performed for SOFC hybrid systems for ammonia-fueled ships.

1. Introduction

The International Maritime Organization (IMO) presented a strategy to reduce carbon intensity (CI) by 70% and greenhouse gas (GHG) emissions by 50% by 2050 compared with 2008 for each vessel [1]. Currently, vessels must satisfy the energy efficiency ship index (EEXI), a technical regulation, and the carbon intensity indicator (CII), an operational regulation [2].

Shipbuilding and shipping industries are actively conducting research and development to respond to these regulations; fuel cells are considered as one of several alternatives. A fuel cell is a device that generates electricity by electrochemical reactions with fuel [3]. It is highly efficient compared to fossil fuel systems and can greatly reduce air pollutants such as CO₂, NO_x, SO_x, and particulate matter because there is no combustion process [4]. Ship propulsion technologies using fuel cells have received considerable attention.

A solid oxide fuel cell (SOFC) uses an oxide ion-conducting electrolyte [5]. The greatest feature of the SOFC is a high operating temperature, approximately 700–1000 °C [6]. An SOFC is capable of internal fuel reforming; thus, an external reformer is not essential, and the reaction is fast [7]. Moreover, it is a highly fuel-flexible, highly efficient, and eco-friendly energy generation device with significant potential [8].

SOFCs have a high operating temperature; thus, additional equipment can be used to increase the overall system efficiency. As a representative example, a system for driving a gas turbine (GT) using the waste energy from a fuel cell can be configured. The medium-low temperature thermal energy discharged from a gas turbine can be recovered through the organic Rankine cycle (ORC). This power generation system is known as the SOFC-GT-ORC hybrid system [9]. The SOFC-GT-ORC hybrid system can increase the efficiency compared to a simple SOFC power generation system and has been studied extensively.

Most studies on SOFC have considered hydrogen or methane fuel cells. The use of hydrogen energy faces many difficulties in terms of production, storage, transportation, and application [10]. Because methane contains carbon atoms, it may be difficult to satisfy the GHG strategy required by the IMO. Ammonia is inexpensive, easy to handle, carbon-free, has a higher energy density than hydrogen, and is emerging as a promising fuel for SOFC power generation [11,12].

Studies on SOFC power-generation systems using ammonia fuel have been conducted at the Clean Energy Research Laboratory of the University of Ontario Institute of Technology. Ishak et al. [13] presented a direct ammonia SOFC integrated with a gas turbine. In this study, oxygen ion-conducting solid oxide fuel cells (O-SOFCs) and hydrogen proton-conducting solid oxide fuel cells (H-SOFCs) were considered. At an operating temperature of 1073 K and pressure of 500 kPa, the energy and exergy efficiencies of the H-SOFC were 81.1% and 74.3%, respectively; those of the O-SOFC were 76.7% and 69.9%, respectively. Siddiqui and Dincer [14] proposed a solar-based multigeneration system integrated with an ammonia fuel cell and an SOFC-GT cycle. Thermodynamic analysis showed that the energy and exergy efficiencies of the system were 68.5% and 55.9%, respectively. Al-Hamed and Dincer [15] proposed an ammonia-based SOFC-GT-ORC system with an absorption chiller for clean rail electric transportation. The optimized system achieved energy and exergy efficiencies of 71.0% and 76.8%, respectively. Ezzat and Dincer [16] proposed a system in which the SOFC-GT mainly produced power, with additional power generated through the Rankine cycle. The residual energy of the exhaust gas was used to operate the absorption chiller system; the electricity generated in the Rankine cycle electrolyzed ammonia into hydrogen. The energy and exergy efficiencies of this system were 58.78% and 50.66%, respectively. Al-Hamed and Dincer [17] presented a new system that produced power using ammonia and operated passenger cars using hydrogen. The uniqueness of this system was that it used waste heat from an SOFC hybrid system to separate ammonia into hydrogen. The thermodynamic evaluation showed that the total energy and exergy efficiencies of this system were 61.2% and 66.3%, respectively.

Ships using ammonia as fuel have recently received considerable attention. An ammonia fuel engine was developed, and a ship propulsion system using an ammonia fuel cell was proposed. Representative studies on SOFC hybrid systems for ammonia-fueled ships include the following. Duong et al. [18] proposed a system in which a steam Rankine cycle and an exhaust gas boiler were added to the rear end of the SOFC-GT. The maximum energy and exergy efficiencies of the system were 64.5% and 61.1%, respectively. Duong et al. [19] proposed an SOFC hybrid system with a gas turbine, steam Rankine cycle, Kalina cycle, and organic Rankine cycle. The energy and exergy efficiencies of the system were 60.4% and 57.3%, respectively. Ryu et al. [20] compared and analyzed the energy efficiency of ammonia and hydrogen used as fuels in an SOFC-GT system for ship propulsion. The energy efficiencies of the system were 60.96% and 64.64% for ammonia and hydrogen, respectively. Ammonia fuel cells have received considerable attention in the maritime industry; future prospects and challenges have been presented [21].

Several studies on fuel cells for ammonia-fueled ships have been conducted in recent years. However, most involved complicated systems and focused only on thermodynamic performance such as energy and exergy efficiency. Complex fuel-cell hybrid systems can improve overall performance but may be difficult to use in ships with limited space, affecting economic feasibility. Wu et al. [22] evaluated the feasibility through economic analysis of an ammonia SOFC system for container ships. The study showed that a rigorous economic evaluation was required to determine practical applicability. A systematic energy, exergy, and economic (3E) analysis of the SOFC hybrid system for ammonia-fueled ships must be performed.

This study does not focus only on increasing thermodynamic efficiency. The purpose of this study was to present a feasible compact system and analyze the thermodynamic performance and economics strictly according to the configuration of the system. To achieve this goal, SOFC-GT and SOFC-GT-ORC hybrid systems for ammonia-fueled ships were simulated. Each system was simulated using a commercial process analysis program; a 3E analysis was performed using analysis models. In addition, parametric analysis was performed by selecting key variables that significantly affected the performance of the system, and optimization was performed using a multi-objective genetic algorithm (GA). The system was optimized by setting the conflicting thermodynamic performance and economics as objective functions. The Pareto curve of each system is presented, and thermodynamic and economic evaluations are performed on the main points. The gains and losses from adding an ORC to the SOFC-GT system were quantitatively evaluated. This study is original in that it systematically used economic analysis methods that have not been adequately performed in previous studies. Since fuel cell hybrid systems using ammonia fuel for ship propulsion have recently received a lot of attention, the analysis method performed in this study may be very necessary. Therefore, it can be a useful reference for the design, manufacturing, and operation of SOFC hybrid systems for ammonia-fueled ships.

2. System Description

This study targets a 3000 DWT general cargo ship using electric propulsion, and the required output is 3800 kW [18]. The ship’s electric power can be supplied by a SOFC hybrid system using ammonia fuel. In this study, SOFC hybrid systems for ammonia-fueled ships corresponding to this concept were studied. Figure 1 shows a schematic of the SOFC-GT (a) and SOFC-GT-ORC (b) hybrid systems for ammonia-fueled ships considered in this study, modified by the system of Ref. [15]. The proposed system is simpler and more feasible than previous systems. By excluding systems for hot water production and absorption chillers, the installation elements and space required for the entire system were reduced, which is advantageous for facility operations.

The SOFC-GT hybrid system (a) is described as follows. Ammonia fuel was heated by the turbine exhaust gas in the fuel regenerator. Some of the fuel flowed into the SOFC; the rest immediately flowed into the combustor. Air in the atmosphere was compressed using an air compressor. The compressed air was heated by the exhaust gas of the turbine in the air regenerator and introduced into the SOFC. The ammonia fuel and air introduced into the SOFC underwent an electrochemical reaction, producing power in the SOFC. Along with the exhaust gas, the fuel and air not react in the SOFC flowed into the combustor. The substances entering the combustor underwent chemical reactions to produce exhaust gases. The exhaust gas from the combustor flowed into the GT to generate additional power. The gas turbine and air compressor were assumed to be coaxially connected. The GT exhaust gas passes through the air and fuel regenerators to increase their temperatures.

The SOFC-GT-ORC hybrid system (b) recovers thermal energy from the exhaust gas discharged from the SOFC-GT system using the ORC. The exhaust gas flows into the ORC evaporator and exits while evaporating the working fluid circulating in the cycle. The evaporated working fluid drives the ORC turbine to generate electricity. The working fluid that drives the ORC turbine is condensed via heat exchange with the cooling water in the condenser. The condensed working fluid flows back into the evaporator after the pressure is increased through the ORC pump.

3. System Modeling

3.1. Energy and Exergy Model

In this study, energy and exergy analyses were performed according to the first and second laws of thermodynamics for a SOFC-GT-ORC hybrid system for ammonia-fueled ships. The energy analysis model can be expressed by Equations (1) and (2), which imply that the law of conservation of mass and energy must be established for the control volume of each component [23]. Energy analysis enables the calculation of the output ($\dot{W}$) and heat transfer rate ($\dot{Q}$) of each component using the continuity equation and energy balance [24]. According to Equations (1) and (2), the energy analysis models for main components can be defined as shown in

Table 1. Energy analysis models for main components in the system.

Component	Energy Analysis Model
Turbine	$\dot{W}=\dot{m}\left(h_{in}-h_{out}\right)$
Compressor/Pump	$\dot{W}=\dot{m}\left(h_{out}-h_{in}\right)$
Heat Exchanger	$\dot{Q}={\dot{m}}_{hot}\left(h_{hot,in}-h_{hot,out}\right)={\dot{m}}_{cold}\left(h_{cold,out}-h_{cold,in}\right)$

. Energy analysis methods for SOFC and combustion, which require an explanation of chemical reactions, are mentioned in detail in Section 3.2.

$$\sum {\dot{m}}_{in}=\sum {\dot{m}}_{out}$$

(1)

$$\sum {\dot{m}}_{in}{h}_{in}+\sum {\dot{Q}}_{in}+\sum {\dot{W}}_{in}=\sum {\dot{m}}_{out}{h}_{out}+\sum {\dot{Q}}_{out}+\sum {\dot{W}}_{out}$$

(2)

The exergy analysis model can be expressed by Equation (3), which represents the exergy balance of the control volume [25]. Exergy analysis enables the calculation of the exergy destruction rate (${\dot{E}}_D$) in each component using an exergy balance [24]. In the exergy analysis, the specific exergy ($e$) can be expressed as the sum of the physical exergy ($e^{ph}$) and chemical exergy ($e^{ch}$), as shown in Equation (4). Physical exergy ($e^{ph}$) can be defined as in Equation (5), where $h_0$ and $s_0$ represent enthalpy and entropy, respectively, in the reference state (1 atm, 25 °C) [24]. The chemical exergy ($e^{ch}$) was considered only for the ammonia fuel; the value was obtained from a study by Siddiqui and Dincer [26]. The chemical exergy values of other substances are very small compared with that of ammonia fuel [15]. According to Equations (3)–(5), the exergy analysis models for the main components in the system are shown in

Table 2. Exergy analysis models for main components in the system.

Component	Exergy Analysis Model
SOFC	${\dot{E}}_D=\sum {\dot{m}}_{in}{e}_{in}-\sum {\dot{m}}_{out}{e}_{out}-\dot{W}$
Combustor	${\dot{E}}_D=\sum {\dot{m}}_{in}{e}_{in}-{\dot{m}}_{out}{e}_{out}$
Turbine	${\dot{E}}_D=\dot{m}\left(e_{in}-e_{out}\right)-\dot{W}$
Compressor/Pump	${\dot{E}}_D=\dot{m}\left(e_{in}-e_{out}\right)+\dot{W}$
Heat Exchanger	${\dot{E}}_D={\dot{m}}_{hot}\left(e_{hot,in}-e_{hot,out}\right)+{\dot{m}}_{cold}\left(e_{cold,in}-e_{cold,out}\right)$

.

$$\sum {\dot{Q}}_{in}\left(1-\frac{T_0}{T_{in}}\right)+\sum {\dot{m}}_{in}{e}_{in}+{\dot{W}}_{in}=\sum {\dot{Q}}_{out}\left(1-\frac{T_0}{T_{out}}\right)+\sum {\dot{m}}_{out}{e}_{out}+{\dot{W}}_{out}+{\dot{E}}_D$$

(3)

$$e=e^{ph}+e^{ch}$$

(4)

$$e^{ph}=\left(h-h_0\right)-T_0\left(s-s_0\right)$$

(5)

The thermodynamic performance evaluation of the entire system is expressed as energy efficiency (${\eta }_{en,overall}$) and exergy efficiency (${\eta }_{ex,overall}$), expressed as Equations (6) and (7), respectively [15].

$${\eta }_{en,overall}=\frac{{\dot{W}}_{total}}{{\dot{m}}_1{HHV}_f}$$

(6)

$${\eta }_{ex,overall}=\frac{{\dot{W}}_{total}}{{\dot{m}}_1{ex}_1}$$

(7)

3.2. SOFC-GT Model

The thermodynamic performance evaluation method for the SOFC-GT model is described as follows. In ammonia-fueled ships, the fuel entering the SOFC is ammonia. Ammonia readily decomposes into $H_2$ and $N_2$ at high temperatures and is completely converted above 873 K [18]. In this study, the fuel cell was assumed to be an O-SOFC based on Ref. [12], and ammonia was directly decomposed through internal reforming. The chemical reaction on the anode side can be defined using Equations (8) and (9) [12].

$$2{NH}_3\to N_2+3H_2$$

(8)

$$H_2+O^{2-}\to H_{2}O+2e^{-}$$

(9)

The chemical reaction on the cathode side can be expressed as Equation (10) [12].

$$0.5O_2+2e^{-}\to O^{2-}$$

(10)

Based on Equations (8)–(10), the overall chemical reaction equation of an SOFC using ammonia fuel is given by Equation (11) [15]. $U$ and $\lambda$ represent the utilization factor and excess air factor, respectively [15,27].

$$\begin{array}{c}{NH}_3+0.75\lambda ·\left(O_2+3.76N_2\right)\to \\ \left(1-U\right)·{NH}_3+1.5U·H_{2}O+0.75\left(\lambda -U\right)·O_2+\left(2.82\lambda +0.5U\right)·N_2\end{array}$$

(11)

The chemical reaction equation in the combustor can be expressed as Equation (12) [15]; $\alpha$ represents the fuel flow ratio and is defined in Equation (13) [15,27].

$$\begin{array}{c}\alpha ·{NH}_3+\left(1-U\right)·{NH}_3+1.5U·H_{2}O+0.75\left(\lambda -U\right)·O_2+\left(2.82\lambda +0.5U\right)·N_2\to \\ 1.5\left(1+\alpha \right)·H_{2}O+0.75\left(\lambda -\left(1+\alpha \right)\right)·O_2+\left(2.82\lambda +0.5\left(1+\alpha \right)\right)·N_2\end{array}$$

(12)

$$\alpha =\frac{{\dot{m}}_4}{{\dot{m}}_2}$$

(13)

The overall chemical reaction equation of the SOFC and combustor can be expressed as Equation (14) [15].

$$\begin{array}{c}\left(1+\alpha \right)·{NH}_3+2\lambda ·\left(O_2+3.76N_2\right)\to \\ 1.5\left(1+\alpha \right)·H_{2}O+0.75\left(\lambda -\left(1+\alpha \right)\right)·O_2+\left(2.82\lambda +0.5\left(1+\alpha \right)\right)·N_2\end{array}$$

(14)

The operating voltage ($V$) can be defined according to the theoretical voltage ($V_0$), Nernst loss, and loss voltage ($V_{loss}$), as shown in Equation (15) [28]. The theoretical voltage, Nernst loss, and loss voltage can be expressed using Equations (16)–(18) [29].

$$V=V_0+Nernst loss-V_{loss}$$

(15)

$$V_0=\frac{-∆G}{nF}$$

(16)

$$Nernst loss=\frac{RT}{nF}\ln \left(\frac{P_{H_2}{P}_{O_2}^{0.5}}{P_{H_{2}O}}\right)$$

(17)

$$V_{loss}=V_{ohm}+V_{act}+V_{conc}$$

(18)

In Equation (16), the Gibbs free energy ($\Delta G$) can be calculated using Equation (19), using the operating temperature of the fuel cell [30]. $n$, $F$, and $R$ denote the number of electrons, the Faraday constant, and the gas constant, respectively.

$$\begin{array}{ll}∆G=& -57093.6-4.9287T+2.2945T·\mathit{ln}\left(T\right)+4.4925·{10}^{-4}{T}^2-4.032·{10}^{-7}{T}^3\\ & +6.7288·{10}^{-11}{T}^4\end{array}$$

(19)

The ohmic loss ($V_{ohm}$), activation loss ($V_{act}$), and concentration loss ($V_{conc}$) were defined according to Refs. [31,32].

Table 3. Equations for ohmic loss, activation loss, and concentration loss for SOFC.

Category	Equations	Reference
$\mathrm{Ohmic} \mathrm{loss} (V_{ohm}$)		Doherty et al. [31]
Anode	$V_{ohm,A}=\frac{i·{\rho }_A{\left(A·\pi ·D_m\right)}^2}{8·t_A}$
Cathode	$V_{ohm,C}=\frac{i·{\rho }_C{\left(\pi ·D_m\right)}^2}{8·t_C}·A\left[A+2\left(1-A-B\right)\right]$
Electrolyte	$V_{ohm,E}={i·\rho }_E·t_E$
Interconnection	$V_{ohm,Int}={i·\rho }_{Int}\left(\pi ·D_m\right)\frac{t_{Int}}{w_{Int}}$
$\mathrm{Activation} \mathrm{loss} (V_{act}$)		Eveloy et al. [32]
Anode	$V_{act,A}=\frac{2RT}{nF}{\sinh }^{-1}\left(\frac{i}{2i_{o,A}}\right)$
	$i_{o,A}={\gamma }_A\left(\frac{P_{H_2}}{P_0}\right)\left(\frac{P_{H_{2}O}}{P_0}\right)exp\left(-\frac{E_{act,A}}{RT}\right)$
Cathode	$V_{act,C}=\frac{2RT}{nF}{\sinh }^{-1}\left(\frac{i}{2i_{o,C}}\right)$ $i_{o,C}={\gamma }_C{\left(\frac{P_{O_2}}{P_0}\right)}^{0.25}exp\left(-\frac{E_{act,C}}{RT}\right)$
$\mathrm{Concentration} \mathrm{loss} (V_{conc}$)		Eveloy et al. [32]
Anode	$V_{conc,A}=-\frac{RT}{nF}\ln \left(1-\frac{i}{i_{l,A}}\right)$
Cathode	$V_{conc,C}=-\frac{RT}{nF}\ln \left(1-\frac{i}{i_{l,C}}\right)$

presents the equations related to the voltage losses used in this study.

The current generated in the SOFC can be expressed as Equation (20) [32]; $n$ and $q$ represent the number of electrons and the molar flow rate of hydrogen reacting in the SOFC, respectively.

$$I=nqF=iA$$

(20)

The DC power of the SOFC can be expressed by Equation (21) using the operating voltage and current calculated in Equations (15) and (20). The AC power of the SOFC can be defined by Equation (22) using the inverter efficiency (${\eta }_{inv}$) [13]. The efficiency of the SOFC can be expressed as Equation (23) [15].

$${\dot{W}}_{SOFC,DC}=VI$$

(21)

$${\dot{W}}_{SOFC,AC}={\eta }_{inv}VI$$

(22)

$${\eta }_{SOFC}=\frac{{\dot{W}}_{SOFC,AC}}{{\dot{m}}_3{h}_3+{\dot{m}}_7{h}_7-{\dot{m}}_8{h}_8-{\dot{m}}_9{h}_9}$$

(23)

The net power of a gas turbine driven by the combustor exhaust gas can be expressed as Equation (24) using the turbine output and the required power of the compressor.

$${\dot{W}}_{GT,net}={\dot{W}}_{Turb}-{\dot{W}}_{Comp}$$

(24)

In the SOFC-GT hybrid system, the total output can be expressed as the sum of the SOFC AC power and GT net output, as shown in Equation (25).

$${\dot{W}}_{total}={\dot{W}}_{SOFC,AC}+{\dot{W}}_{GT,net}$$

(25)

3.3. Organic Rankine Cycle Model

The thermodynamic performance of the SOFC-GT-ORC hybrid system should be evaluated by considering the ORC model. The net output of the ORC can be expressed by Equation (26) using the turbine output and the required power of the pump. The ORC efficiency can be expressed as Equation (27) [15].

$${\dot{W}}_{ORC,net}={\dot{W}}_{Turb,ORC}-{\dot{W}}_{Pump,ORC}$$

(26)

$${\eta }_{ORC}=\frac{{\dot{W}}_{ORC,net}}{{\dot{Q}}_{Evap}}$$

(27)

In the SOFC-GT-ORC hybrid system, the total output can be expressed as the sum of the SOFC AC power, GT net output, and ORC net output, as shown in Equation (28).

$${\dot{W}}_{total}={\dot{W}}_{SOFC,AC}+{\dot{W}}_{GT,net}+{\dot{W}}_{ORC,net}$$

(28)

3.4. Economic Model

Economic analysis of the SOFC hybrid system for ammonia-fueled ships was not well-performed in previous studies. The models for rigorous economic analysis are described as follows. The cost rate (${\dot{Z}}_k$) of each component is the cost per hour ($/h), and is defined in Equation (29) [33]. $Z_k$ of each component can be obtained using the cost function specified in

Table 4. Cost functions for SOFC-GT-ORC hybrid system.

Component	Cost Functions	Reference
SOFC	$Z_{SOFC}=A_{SOFC}(2.96T_{SOFC}-1907)$	Eveloy et al. [32]
Combustor	$Z_{Comb}=\left(\frac{46.08{\dot{m}}_{in}}{0.995-P_{out}/P_{in}}\right)\left[1+\mathrm{e}\mathrm{x}\mathrm{p}(0.018T_{out}-26.4)\right]$
Gas Turbine	$Z_{Turb}=\left(-98.328\ln \left({\dot{W}}_{Turb}\right)+1318.5\right){\dot{W}}_{Turb}$
Air compressor	$Z_{Comp}=\frac{39.5{\dot{m}}_{in}}{0.9-{\eta }_{Comp}}\left(\frac{P_{out}}{P_{in}}\right)\ln \left(\frac{P_{out}}{P_{in}}\right)$
Heat Exchanger	$Z_{HEX}=4122{\left(\frac{{\dot{m}}_{in}\left(h_{in}-h_{out}\right)·1000}{18∆T_{HEX}}\right)}^{0.6}$	Wang et al. [33]
ORC	$Z_{ORC}=2345000\left(\frac{{\dot{W}}_{ORC,net}}{1115 kW}\right)$	Eveloy et al. [32]

[32,33]. $\varphi$ and $N$ are the maintenance factor and yearly operating hours, assumed to be 1.06 and 6000 h, respectively [33]. The capital recovery factor ($CRF$) can be defined using Equation (30) [33,34]. $i$ and $n$ represent the interest rate and lifetime assumed to be 5% and 10 years, respectively [33]. The total cost rate ($TCR$, Equation (31)) of the system can be obtained by adding all cost rates (${\dot{Z}}_k$) of each component [34].

$${\dot{Z}}_k=\frac{Z_k·CRF·\varphi }{N}$$

(29)

$$CRF=\frac{i{\left(i+1\right)}^n}{{\left(i+1\right)}^n-1}$$

(30)

$$TCR=\sum {\dot{Z}}_k$$

(31)

4. Simulation Conditions and Default Results

4.1. Simulation Conditions of SOFC-GT Hybrid System

In this study, the system was simulated using Aspen HYSYS v12.1 [35] and analyzed in a steady state. The Peng–Robinson equation was used as the equation of state (EOS). The simulation conditions for the SOFC-GT hybrid system are described in Refs. [15,18] and are presented in

Table 5. Simulation conditions for SOFC-GT hybrid system.

Parameter	Unit	Value
SOFC—General [15,18]
$\mathrm{Fuel} \mathrm{inlet} \mathrm{temperature} \left(T_1\right)$	K	303.0
$\mathrm{Fuel} \mathrm{inlet} \mathrm{pressure} \left(P_1\right)$	kPa	400.0
$\mathrm{Fuel} \mathrm{temperature} \mathrm{after} \mathrm{regenerator} \left(T_2\right)$	K	800.0
$\mathrm{Flow} \mathrm{ratio} \left(\alpha \right)$	-	0.15
$\mathrm{Air} \mathrm{inlet} \mathrm{temperature} \left(T_5\right)$	K	303.0
$\mathrm{Air} \mathrm{inlet} \mathrm{pressure} \left(P_5\right)$	kPa	100.0
Air compressor pressure ratio	-	4.0
$\mathrm{Air} \mathrm{temperature} \mathrm{after} \mathrm{regenerator} \left(T_7\right)$	K	765.8
SOFC operating temperature	K	900.0
SOFC operating pressure	kPa	400.0
$\mathrm{Current} \mathrm{density} \left(i\right)$	A/m2	1750
$\mathrm{Utilization} \mathrm{factor} \left(U\right)$	-	0.8
$\mathrm{Excess} \mathrm{air} \mathrm{factor} \left(\lambda \right)$	-	1.4
$\mathrm{DC}/\mathrm{AC} \mathrm{inverter} \mathrm{efficiency} \left({\eta }_{inv}\right)$	%	98.0
Gas turbine [15]
Gas turbine pressure ratio	-	4.0
Gas turbine isentropic efficiency	%	90.0

.

The voltage loss must be calculated to obtain the operating voltage of the SOFC. The simulation conditions for ohmic, activation, and concentration losses, which constitute the total voltage loss of a SOFC, are described in Refs. [31,32] and are presented in

Table 6. Simulation conditions for SOFC voltage loss.

Parameter	Unit	Value
SOFC—Ohmic loss [31]
$\mathrm{Cell} \mathrm{mean} \mathrm{diameter} \left(D_m\right)$	m	0.022
$\mathrm{Anode} \mathrm{thickness} \left(t_A\right)$	m	0.0001
$\mathrm{Cathode} \mathrm{thickness} \left(t_C\right)$	m	0.0022
$\mathrm{Electrolyte} \mathrm{thickness} \left(t_E\right)$	m	0.00004
$\mathrm{Interconnection} \mathrm{thickness} \left(t_{Int}\right)$	m	0.000085
$\mathrm{Interconnection} \mathrm{width} \left(w_{Int}\right)$	m	0.009
$\mathrm{Anode} \mathrm{resistivity} \left({\rho }_A\right)$	Ω·m	2.98·${10}^{-5} \exp (-1392/T)$
$\mathrm{Cathode} \mathrm{resistivity} \left({\rho }_C\right)$	Ω·m	8.114·${10}^{-5} \exp (600/T)$
$\mathrm{Electrolyte} \mathrm{resistivity} \left({\rho }_E\right)$	Ω·m	2.94·${10}^{-5} \exp (10350/T)$
$\mathrm{Interconnection} \mathrm{resistivity} \left({\rho }_{Int}\right)$	Ω·m	0.025
A/B	-	0.804/0.13
SOFC—Activation loss [32]
$\mathrm{Pre}-\mathrm{exponential} \mathrm{coefficient} \mathrm{for} \mathrm{anodic} \mathrm{exchange} \mathrm{current} \mathrm{density} \left({\gamma }_A\right)$	A/m2	5.5·108
$\mathrm{Anodic} \mathrm{activation} \mathrm{energy} \left(E_{act,A}\right)$	J/mol	1.0·105
$\mathrm{Pre}-\mathrm{exponential} \mathrm{coefficient} \mathrm{for} \mathrm{cathodic} \mathrm{exchange} \mathrm{current} \mathrm{density} \left({\gamma }_C\right)$	A/m2	7.0·108
$\mathrm{Cathodic} \mathrm{activation} \mathrm{energy} \left(E_{act,C}\right)$	J/mol	1.2·105
SOFC—Concentration loss [32]
$\mathrm{Anodic} \mathrm{limiting} \mathrm{current} \mathrm{density} \left(i_{l,A}\right)$	A/m2	2.99·104
$\mathrm{Cathodic} \mathrm{limiting} \mathrm{current} \mathrm{density} \left(i_{l,C}\right)$	A/m2	2.16·104

.

4.2. Validation of SOFC-GT Models

In this study, it was necessary to validate whether the SOFC-GT model was appropriately simulated. The results were compared with those in Ref. [15], which is referenced in the system simulation. For comparison with a performance level similar to that in Ref. [15], the molar flow rate of the ammonia fuel introduced into the SOFC was set to 50.0 kgmole/h. The results are presented in

Table 7. Validation results for SOFC-GT hybrid system.

Parameter	Results	Ref. [15]	Difference
SOFC power	2088 kW	2158 kW	3.4%
SOFC efficiency	66.5%	65.0%	1.5%
GT net power	755.3 kW	782.3 kW	3.6%

, which shows that the performance errors of the SOFC and GT are low. That is, the SOFC-GT model and the conditions used in this study can be considered appropriate.

4.3. Simulation Conditions of the ORC

The analysis conditions for the SOFC-GT in the SOFC-GT-ORC hybrid system were the same. The simulation conditions of the ORC are described in Refs. [15,36] and are presented in

Table 8. Simulation conditions for ORC.

Parameter	Unit	Value
Working fluid	-	Ammonia
$\mathrm{Turbine} \mathrm{inlet} \mathrm{temperature} \left(T_{15}\right)$	K	600.0
$\mathrm{Turbine} \mathrm{inlet} \mathrm{pressure} \left(P_{15}\right)$	kPa	5000
$\mathrm{Condensing} \mathrm{pressure} \left(P_{17}\right)$	kPa	1000
Condenser exit vapor quality	-	0
$\mathrm{Cooling} \mathrm{water} \mathrm{temperature} (T_{19}$)	K	293.0
$\mathrm{Cooling} \mathrm{water} \mathrm{temperature} (P_{19}$)	kPa	200
Evaporator pinch point temperature difference	K	5.0
Condenser pinch point temperature difference	K	5.0
Turbine isentropic efficiency	%	90.0
Pump adiabatic efficiency	%	80.0

. The ORC using high-pressure ammonia in the SOFC hybrid system can replace the large and complicated steam Rankine cycle [15]. Thus, the working fluid of the ORC in this study was ammonia.

4.4. Default Results of SOFC-GT-ORC Hybrid System

The subject of this study is a fuel cell for ammonia-fueled ships. According to Refs. [18,19,20], ammonia-fueled ships require an output of 3800 kW. In this study, the molar flow rate of the ammonia fuel introduced into the SOFC was set at 93.0 kgmole/h to make the output of the SOFC 3800 kW.

Table 9. Default results for SOFC-GT-ORC hybrid system.

Parameter	Unit	Value
$\mathrm{SOFC} \mathrm{electric} \mathrm{power} \left({\dot{W}}_{SOFC,AC}\right)$	kW	3806
$\mathrm{SOFC} \mathrm{efficiency} \left({\eta }_{SOFC}\right)$	%	65.2
$\mathrm{GT} \mathrm{net} \mathrm{power} \left({\dot{W}}_{GT,net}\right)$	kW	1405
$\mathrm{ORC} \mathrm{net} \mathrm{power} \left({\dot{W}}_{ORC,net}\right)$	kW	444.2
$\mathrm{ORC} \mathrm{efficiency} \left({\eta }_{ORC}\right)$	%	18.0
$\mathrm{Overall} \mathrm{energy} \mathrm{efficiency} \left({\eta }_{en,overall}\right)$	%	49.2
$\mathrm{Overall} \mathrm{exergy} \mathrm{efficiency} \left({\eta }_{ex,overall}\right)$	%	54.5
$\mathrm{Overall} \mathrm{exergy} \mathrm{destruction} \left({\dot{E}}_{D,overall}\right)$	kW	4621
Total cost rate (TCR)	$/h	112.5

presents the simulation results for the SOFC-GT-ORC hybrid system. These results are the default values that reflect the system modeling conditions.

5. Analysis of Key Variables

In this study, a 3E analysis was performed using key variables affecting the performance of the simulated system. The current density ($i$) and flow ratio ($\alpha$, Equation (13)) were considered in the SOFC-GT; the turbine inlet temperature ($T_{15}$) and pressure ($P_{15}$) were determined in the ORC. In the SOFC-GT hybrid system, the influences of key SOFC variables were examined. In the SOFC-GT-ORC hybrid system, changes according to the key ORC variables were confirmed. Analysis according to the key variables was based on the system models and simulation conditions specified in Section 3 and Section 4.

5.1. SOFC-GT Hybrid System

Figure 2 shows the analysis results of the SOFC-GT hybrid system with respect to the current density ($i$). Figure 2a shows the electrical output and efficiency of the SOFC. As the current density ($i$) increased, the performance first improved and then decreased. The maximum performance was observed at a current density of 1300 A/m²; the SOFC electric power and efficiency were 3933 kW and 67%, respectively. Figure 2b shows the SOFC-GT power and energy efficiency; Figure 2c shows the SOFC-GT exergy efficiency and destruction rate. Figure 2b,c shows the maximum performance of the system with a current density of 1300 A/m². The corresponding SOFC-GT power and energy efficiency were 5338 kW and 46.4%, respectively. The exergy efficiency and destruction rate of the SOFC-GT were 51.1% and 3930 kW, respectively. From these results, it is observed that there is an optimal current density at which the maximum thermodynamic performance of the system can be expected. Figure 2d shows the TCR of the SOFC and SOFC-GT. Because the current in an SOFC is determined by the number of electrons, molar flow rate, and Faraday’s constant, it remains constant even when the current density changes. Here, a high current density implies that a smaller area is required for the same current, reducing the cost of the SOFC. Thus, the TCR of the SOFC and SOFC-GT tended to decrease as the current density increased.

Figure 3 shows the analysis results for the SOFC-GT hybrid system according to the flow ratio ($\alpha$). As shown in Figure 3a, as the flow ratio increased, the electrical power of the SOFC decreased. An increase in the flow ratio implies that the flow rate of the ammonia fuel entering the SOFC decreases according to Equation (13). The SOFC efficiency was constant at 65% according to the flow ratio because it was assumed that the flow rate of air was adjusted according to the flow rate of the fuel entering the SOFC. In the SOFC, fuel and air were simulated to react at a constant rate according to Equation (11). Figure 3b shows that the power and energy efficiencies of the SOFC-GT decreased as the flow ratio increased. As the flow ratio increased, the flow rate of fuel into the combustor increased, and the GT output increased. However, a decrease in the SOFC output had a greater effect, resulting in a decrease in the power and efficiency of the entire system. Figure 3c shows that the exergy efficiency and destruction rate decreased as the flow ratio increased. This means that as the amount of fuel entering the SOFC decreased, the irreversibility decreased with the efficiency of the system. Figure 3d shows that the TCR of the SOFC and SOFC-GT decreased with increasing flow ratio. A decrease in the fuel flow toward the SOFC resulted in a decrease in the current. Because the current density was constant, the reduced current reduced the SOFC area. The area reduction in the SOFC resulted in a reduced system cost. These results indicate that the thermodynamic performance and economics are inversely proportional to each other according to the change in the flow ratio.

5.2. SOFC-GT-ORC Hybrid System

Figure 4 shows the analysis results for the SOFC-GT-ORC hybrid system according to the inlet temperature of the ORC. Figure 4a shows that the net power and efficiency of the ORC increased as the inlet temperature of the ORC turbine increased. The enthalpy of the ammonia flowing into the turbine increased as the temperature increased, resulting in an increase in the ORC turbine output. As shown in Figure 4b,c, as the turbine inlet temperature increased, the total power, energy efficiency, and exergy efficiency of the SOFC-GT-ORC increased and the exergy destruction rate decreased. The thermodynamic performance of the entire system improved as the inlet temperature of the ORC turbine increased because the increase in the output of the ORC turbine improved the performance of both the ORC and the entire system. The results of the economic analysis of the system are shown in Figure 4d. As the inlet temperature of the ORC turbine increased, the TCR of the ORC and SOFC-GT-ORC increased slightly because an increase in the ORC output increased the cost. That is, increasing the inlet temperature of the ORC turbine can improve the thermodynamic performance of the system, but incurs additional costs.

Figure 5 shows the analysis results of the SOFC-GT-ORC hybrid system according to the inlet pressure of the ORC turbine. In Figure 5a, as the inlet pressure of the ORC turbine increases, the net power and efficiency of the ORC increase. An increase in the pressure of the ammonia flowing into the turbine can be expected to increase the enthalpy and output of the ORC turbine, but can also increase the required power of the ORC pump. Consequently, an increase in the output of the ORC turbine has a more profound effect on the ORC, resulting in improved ORC performance. In Figure 5b,c, increasing the inlet pressure of the ORC increases the total power, energy efficiency, and exergy efficiency of the SOFC-GT-ORC, while decreasing the exergy destruction rate. Increasing the inlet pressure of the ORC turbine improves the thermodynamic performance of the entire system as well as the ORC, similar to increasing the inlet temperature of the ORC turbine. Figure 5d shows that as the inlet pressure of the ORC turbine increases, the TCR of the ORC and SOFC-GT-ORC increase. This is because the cost increases as the power of the ORC increases. In other words, as in the previous results, the economic cost of the system is proportional to its increase in output.

6. Multi-Objective Optimization for Hybrid Systems

The results of the system analysis based on the key variables indicated that the performance and economics of the system were generally inversely proportional. In this study, a quantitative evaluation was performed through optimization by considering conflicting factors.

Multi-objective optimization was performed for SOFC-GT and SOFC-GT-ORC hybrid systems using a GA. Figure 6 shows a schematic of the multi-objective optimization process performed by interoperating Aspen HYSYS v12.1 [35] and MathWorks MATLAB R2023a [37]. When the GA was executed in MATLAB, multi-objective optimization of the system was performed in HYSYS [24]. Multi-objective optimization essentially requires multiple objective functions that conflict with each other. As explained previously, the thermodynamic performance and economics of the system were inversely proportional. In this study, the exergy efficiency, which represents the thermodynamic performance, and TCR, which represents the economic feasibility, were determined as the objective functions of the GA. The GA performed optimization according to each objective function and presented a Pareto curve. The main GA parameters for the multi-objective optimization were obtained from the MATLAB user manual [37] and are presented in

Table 10. Genetic algorithm parameter for multi-objective optimization.

Parameter	Value
Population size	50
Maximum generations	200 Number of variables
Crossover fraction	0.8
Function tolerance	10−4

. Other GA parameters were set to their respective default values.

Optimization of the system is performed by modifying the independent variables, and details related to them are as follows. The boundary ranges of the independent variables for optimization of the SOFC-GT hybrid system are shown in Equations (32) and (33). The variables and ranges considered were the same as those used in the key variable analysis of the SOFC.

$$1000\le Current density \left(i\right)\le 2000$$

(32)

$$0.11\le Flow ratio \left(\alpha \right)\le 0.25$$

(33)

In the optimization of the SOFC-GT-ORC hybrid system, ORC-related independent variables should also be considered, along with Equations (32) and (33). Equations (34) and (35) represent the boundary ranges of the independent variables for optimization, which were the same as those in the key variable analysis of the ORC.

$$460\le Turbine inlet temperature \left(T_{15}\right)\le 740$$

(34)

$$3000\le Turbine inlet pressure \left(P_{15}\right)\le 7000$$

(35)

7. Analysis of Multi-Objective Optimization Results

Figure 7 shows the Pareto curves according to the multi-objective optimization using the GA. These curves are expressed by connecting the optimized points with dotted lines. Figure 7a,b show the results for the SOFC-GT and SOFC-GT-ORC hybrid systems, respectively. The main points were selected to quantitatively analyze the two systems. Point A with the highest exergy efficiency and TCR, and point B with the lowest exergy efficiency were selected for comparative analysis.

Table 11. Results of multi-objective optimization for SOFT-GT and SOFC-GT-ORC hybrid systems.

Parameter	Unit	SOFC-GT (A)	SOFC-GT (B)	SOFC-GT-ORC (A)	SOFC-GT-ORC (B)
$i$	A/m2	1350.7	1947.8	1301.2	1917.9
$\alpha$	-	0.11	0.25	0.17	0.22
$T_{15}$	K	-	-	491.1	509.1
$P_{15}$	kPa	-	-	6515.1	4672.3
${\dot{W}}_{SOFC,AC}$	kW	4108.8	3270.2	3835.5	3418.4
${\eta }_{SOFC}$	%	67.3	63.3	67.4	63.6
${\dot{W}}_{GT,net}$	kW	1350.0	1538.9	1434.3	1498.3
${\dot{W}}_{ORC,net}$	kW	-	-	480.4	476.8
${\eta }_{ORC}$	%	-	-	18.1	16.2
${\dot{W}}_{overall}$	kW	5458.8	4809.1	5750.2	5393.5
${\eta }_{en,overall}$	%	47.5	41.8	50.0	46.9
${\eta }_{ex,overall}$	%	52.6	46.4	55.4	52.0
${\dot{E}}_{D,overall}$	kW	3951.9	4056.3	4532.8	4894.6
TCR	$/h	113.0	79.8	132.6	104.6

presents detailed results for each main point in Figure 7. A and B in the SOFC-GT hybrid system are compared as follows. The values of current density ($i$) and flow ratio ($\alpha$) of A were optimized to be lower than those of B. In Figure 2, the highest level of thermal efficiency could be expected around 1300 A/m². From Figure 3, the more ammonia fuel introduced into the SOFC, the better the thermodynamic performance of the system. Thus, A had a lower net output of GT than B, but the power and efficiency of SOFC were superior. The total energy and exergy efficiencies of A were 5.7% and 6.2% higher than those of B, respectively. The TCR of B can be lowered by 29.4% to that of A, which is economically advantageous. The cost of the system could be lowered when the current density and flow ratio were large, as identified in the key variable analysis.

A and B in the SOFC-GT-ORC hybrid system are compared as follows. The current density ($i$) and flow ratio ($\alpha$) of A focused on thermodynamic performance were optimized to lower values than those of B focused on economics. Here, the ORC turbine inlet temperature ($T_{15}$) was optimized; A and B had similar values. As shown in Figure 4, this was because the difference between the maximum and minimum values of the exergy efficiency was not large over a wide range of temperatures. The ORC turbine inlet pressure ($P_{15}$) was greater at A than at B because the higher the ORC turbine inlet pressure, the higher the ORC output, as shown in Figure 5. Consequently, A had a higher SOFC and ORC output and efficiency than B. The total energy and exergy efficiencies of A were 3.1% and 3.4% higher, respectively, than those of B. However, the TCR of B was 21.1% less than that of A because the output of the system was reduced, reducing the cost.

This study focused on the changes in performance and economics with the addition of an ORC. Comparison and analysis of the optimization results for the SOFC-GT and SOFC-GT-ORC hybrid systems are presented as follows. The energy and exergy efficiencies of SOFC-GT-ORC (A) were 2.5% and 2.8% higher than those of SOFC-GT (A), respectively. The TCR of SOFC-GT (A) was 14.8% lower than that of SOFC-GT-ORC (A). The energy and exergy efficiencies of SOFC-GT-ORC (B) were 5.1% and 5.6% higher than those of SOFC-GT (B), respectively. The TCR of SOFC-GT (B) was 23.7% lower than that of SOFC-GT-ORC (B). As a result, the thermal efficiency of the SOFC-GT hybrid system was increased by 2–6% by installing an ORC, but the cost increased by 14–24%. In addition, the installation, operation, and maintenance of an ORC may be considered.

Figure 8 shows the exergy destruction rates by component for the SOFC-GT and SOFC-GT-ORC hybrid systems. In the SOFC-GT hybrid system, a large amount of exergy destruction occurs in the SOFC and combustor. In comparison, SOFC-GT (A), in which a large amount of ammonia fuel is introduced into the SOFC, had a 6% higher exergy destruction rate of SOFC than SOFC-GT (B). In SOFC-GT (B), with a large amount of fuel flowing directly into the combustor, the exergy destruction rate of the combustor was 5% higher than that in SOFC-GT (A). From these results, the inflow path of ammonia fuel had a significant influence on the exergy destruction of each component. In an SOFC-GT-ORC system, it is necessary to consider the ORC exergy destruction rate. In both systems, a large amount of exergy destruction occurred in the ORC evaporator, SOFC, and combustor. In the SOFC-GT-ORC hybrid system, the optimal design to reduce the irreversibility of the ORC evaporator, SOFC, and combustor appears to effectively improve system performance. Here, to reduce irreversibility, entropy generation must be reduced as much as possible. In other words, minimizing entropy generation during processes such as friction, mixing, chemical reaction, heat transfer, and mechanical work within the system can be said to be a technology or strategy necessary for optimal design [38].

Figure 9 shows the costs of the equipment in the SOFC-GT and SOFC-GT-ORC hybrid systems. The SOFC had the highest cost. In addition, the cost increased rapidly as the amount of ammonia fuel introduced into the SOFC increased. In the SOFC-GT system, the SOFC cost of (B), where a relatively small amount of fuel flows into the SOFC, is 33.1 $/h cheaper than that of (A). In the SOFC-GT-ORC system, the SOFC cost of (B) is 28.0 $/h less than that of (A). Table 11 shows that if more fuel is introduced into the SOFC, more power can be obtained. However, supplying SOFC fuel beyond the target power required by the ship may cause excessive cost losses. Thus, it is economical to use a moderate amount of SOFC fuel to achieve the target output. Aside from the SOFC, gas turbines account for a large proportion of the cost. The cost of the gas turbine was not significantly different in each case. Thus, the design and operation of SOFCs can effectively improve the efficiency and economy of the system. In the SOFC-GT-ORC hybrid system, the cost of the ORC was approximately $23/h, in excess of $138,000 per year. Thus, the application of the ORC in the SOFC-GT hybrid system must be carefully considered.

8. Conclusions

In response to recently strengthened ship exhaust gas regulations, SOFC hybrid systems have been proposed for ammonia-fueled ships. However, most studies suggested complex systems that focused only on thermodynamic performance, not considering economics.

In this study, after presenting a feasible SOFC hybrid system for ammonia-fueled ships, a 3E analysis was performed to quantitatively identify the thermodynamic performance and economic feasibility according to the configuration of the system. Key variables of the system were selected, a parametric analysis was performed, and multi-objective genetic algorithm optimization was performed using these variables. The Pareto curve of each system was presented, and thermodynamic and economic evaluations were performed on the main points. The main results of the rigorous 3E analysis are summarized as follows.

• The SOFC exhibited excellent thermodynamic performance in the system when the current density was 1300 A/m² and a large amount of ammonia fuel was introduced. Additionally, the higher the inlet temperature and pressure of the ORC turbine, the more advantageous it was in terms of thermal efficiency. However, TCR, which represents economic feasibility, generally increased as the thermodynamic performance increased.
• The SOFC-GT hybrid system with the ORC can increase the thermal efficiency by 2–6%; however, the cost increases by 14–24%.
• In the SOFC-GT-ORC hybrid system, it is advantageous in terms of performance to preferentially reduce the irreversibility of the ORC evaporator together with the SOFC and combustor.
• Thus, it is economical to use SOFC fuel moderately to meet the target output. The cost of the ORC in a SOFC-GT-ORC hybrid system is approximately $23/h, representing over $138,000 per year in the simulation conditions in this study.

This study is unique in that it systematically performed a 3E analysis of SOFC hybrid systems for ammonia-fueled ships, which had not previously been performed. The efficiency improvement and economic loss when adding the ORC to the SOFC-GT hybrid system were quantitatively shown under the conditions assumed in this study. Quantitative economic analysis can contribute to rational decisions about adding the ORC to SOFC-GT hybrid systems for ammonia-fueled ships, and this study shows that the introduction of ORC in the system should be carefully considered. Because this study simultaneously analyzed the performance and economic feasibility of the system, it can serve as a useful reference in the field of electric propulsion ships equipped with SOFC hybrid systems using ammonia fuel.